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Computer-Aided Design
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ACM Transactions on Graphics (TOG)
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ACM Transactions on Graphics (TOG)
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Intersecting quadrics: an efficient and exact implementation
Computational Geometry: Theory and Applications
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Computer Aided Geometric Design
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Journal of Symbolic Computation
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ISCGAV'06 Proceedings of the 6th WSEAS International Conference on Signal Processing, Computational Geometry & Artificial Vision
Using signature sequences to classify intersection curves of two quadrics
Computer Aided Geometric Design
Computing the Voronoi cells of planes, spheres and cylinders in R3
Computer Aided Geometric Design
Intersecting quadrics: an efficient and exact implementation
Computational Geometry: Theory and Applications
A robust algorithm for finding the real intersections of three quadric surfaces
Computer Aided Geometric Design
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Computer-Aided Design
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ICRA'09 Proceedings of the 2009 IEEE international conference on Robotics and Automation
Robustly computing intersection curves of two canal surfaces with quadric decomposition
ICCS'06 Proceedings of the 6th international conference on Computational Science - Volume Part II
Approximating algebraic space curves by circular arcs
Proceedings of the 7th international conference on Curves and Surfaces
Journal of Symbolic Computation
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Levin's method produces a parameterization of the intersection curve of two quadrics in the form p(u) = a(u) ± d(u) √s(u), where a(u) and d(u) are vector valued polynomials, and s(u) is a quartic polynomial. This method, however, is incapable of classifying the morphology of the intersection curve, in terms of reducibility, singularity, and the number of connected components, which is critical structural information required by solid modeling applications. We study the theoretical foundation of Levin's method, as well as the parameterization p(u) it produces. The following contributions are presented in this paper: (1) It is shown how the roots of s(u) can be used to classify the morphology of an irreducible intersection curve of two quadric surfaces. (2) An enhanced version of Levin's method is proposed that, besides classifying the morphology of the intersection curve of two quadrics, produces a rational parameterization of the curve if the curve is singular. (3) A simple geometric proof is given for the existence of a real ruled quadric in any quadric pencil, which is the key result on which Levin's method is based. These results enhance the capability of Levin's method in processing the intersection curve of two general quadrics within its own self-contained framework.